Stability of Neel skyrmions in ultra-thin nanodots considering Dzyaloshinskii-Moriya and dipolar interactions

N Vidal-Silva; A Riveros; J Escrig

doi:10.1016/j.jmmm.2017.07.049

paper

Stability of Neel skyrmions in ultra-thin nanodots considering Dzyaloshinskii-Moriya and dipolar interactions

arXiv:1705.03778 · doi:10.1016/j.jmmm.2017.07.049

Abstract

An analytical expression for the energy of Néel skyrmions in ultra-thin nanodots considering exchange, uniaxial anisotropy, Dzyaloshinskii-Moriya, and dipolar contributions has been obtained. In particular, we have proposed for the Néel skyrmion, a general ansatz for the component of the magnetization perpendicular to the dot, given by $m_{z} (r) = [1 - (r / R_{s})^{n}] / [1 + (r / R_{s})^{n}]$ , where $R_{s}$ is the radius of the skyrmion and $n$ is an integer and even number. As proof of concept, we calculate the energy of a Néel skyrmion in an ultra-thin Co/Pt dot, and we find that the dipolar contribution cannot be neglected and that both Dzyaloshinskii-Moriya interaction and anisotropy play an important role to stabilize the skyrmion. Additionally, we have obtained a good agreement between our analytical calculations and previously published micromagnetic simulations for $n = 10$ . For this reliable value of $n$ , we have obtained that for a Dzyaloshinski Moriya constant $D = 5.5 (m J / m^{2})$ , it is possible to stabilize a Néel skyrmion for $K_{u}$ in the range, $0.4 (M J / m^{3}) < K_{u} < 1.3 (M J / m^{3})$ , whereas for $K_{u} = 0.8 (M J / m^{3})$ , the skyrmion stabilizes for $5.0 (m J / m^{2}) < D < 6.0 (m J / m^{2})$ . Thus, this analytical equation can be widely used to predict stability ranges for the Néel skyrmion in spintronic devices.

10 pages, 6 figures

Stability of Neel skyrmions in ultra-thin nanodots considering Dzyaloshinskii-Moriya and dipolar interactions

Abstract

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